Spherically symmetric Finsler metrics with Scalar Flag Curvature

Finsler metrics of scalar flag curvature and projective invariants

In this paper, we define a new projective invariant and call it W̃ -curvature. We prove that a Finsler manifold with dimension n ≥ 3 is of constant flag curvature if and only if its W̃ -curvature vanishes. Various kinds of projectively flatness of Finsler metrics and their equivalency on Riemannian metrics are also studied. M.S.C. 2010: 53B40, 53C60.

Nonreversible Finsler Metrics of Positive Flag Curvature

Reversible Homogeneous Finsler Metrics with Positive Flag Curvature

In this work, we continue with the classification for positively curved homogeneous Finsler spaces (G/H,F ). With the assumption that the homogeneous space G/H is odd dimensional and the positively curved metric F is reversible, we only need to consider the most difficult case left, i.e. when the isotropy group H is regular in G. Applying the fixed point set technique and the homogeneous flag c...

Randers Metrics of Scalar Flag Curvature

We study an important class of Finsler metrics — Randers metrics. We classify Randers metrics of scalar flag curvature whose S-curvatures are isotropic. This class of Randers metrics contains all projectively flat Randers metrics with isotropic S-curvature and Randers metrics of constant flag curvature.

Finsler Manifolds with Nonpositive Flag Curvature and Constant S-curvature

The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) nonRiemannian Finsler metrics on an open subset in Rn with negative flag curvature and constant S-curvature. In this paper, we are going to show a global rigidity theorem that every Finsler met...